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Volume of Prisms/Transcript
Transcript Title text reads, The Mysteries of Life with Tim and Moby. Tim is lounging on a chair in the backyard. Moby is holding a glass prism. TIM: Don't break that, it's fragile! Moby beeps. A letter appears. Text reads as Tim narrates: Dear Tim and Moby, how do I measure the volume of prisms? From, Marta TIM: 3 dimensional shapes like prisms can seem tricky to measure. Moby beeps. He draws 3-D shapes on the ground with chalk. TIM: And hard to draw. Not that difficult, really. Moby beeps. TIM: Well, measuring the volume, anyway. A prism is a solid with 2 parallel congruent bases. On-screen, a square, a triangle, and several other polygons appear. Each shape is doubled, resulting in 2 identical triangles, 2 identical squares, and so on. Next, each pair of identical shapes is connected by parallel lines. This turns each pair of 2 dimensional polygons into a 3 dimensional prism. TIM: Their sides are parallelograms, and we name prisms by the shapes of their bases. Labels appear above each prism, reading: triangular prism, rectangular prism, pentagonal prism, hexagonal prism, heptagonal prism, and octagonal prism. TIM: Let's start with a regular rectangular prism, also known as a cube. Moby holds up a cube. TIM: This cube has sides that are 10 centimeters long. On-screen, each side of the cube is labeled, 10 centimeters. TIM: Now, the formula for finding the volume of a prism, is the area of the base, times the height. A formula appears, reading, B, times H. TIM: Our base is a square, and the area of a square can be found by multiplying the length times the width. On-screen, the cube rotates to show 1 of its square bases. Each side of the square is labeled, 10 centimeters. TIM: That's 10 centimeters times 10 centimeters; and that's 100 centimeters squared. On-screen, the area of the base is labeled, 100 centimeters squared. The cube rotates to a 3 dimensional view. Its height is labeled, 10 centimeters. TIM: Now we multiply the area of the base times the height of the prism, and get 1,000 centimeters cubed, or 1,000 cubic centimeters. An equation appears, reading, 100 centimeters squared, times 10 centimeters, equals 1,000 centimeters cubed. TIM: Easy enough? Moby beeps. TIM: The same formula, area of the base times height, will work with other rectangular prisms, too. They're just not as easy as a 10 centimeter cube. On-screen, many 3 dimensional shapes appear. All their bases are rectangles, but none of them are cubes. Moby beeps. TIM: Let's try a triangular prism. The formula for calculating the volume is the same: area of the base times the height. On-screen, a triangular prism appears, next to the formula, B, times H. TIM: So first, we find the area of the base. On-screen, the prism rotates to show 1 of its triangular bases. TIM: Hey, Moby, do you remember the formula for a triangle's area? Moby beeps. TIM: Right: one-half of the base... times the height. A formula appears, reading, one-half B, times H. TIM: This triangle has a base of 8 centimeters, and the height is 6 centimeters. On-screen, the triangle's base is labeled, 8 centimeters. Its height is labeled, 6 centimeters. TIM: So, one-half of the base is 4 centimeters, times 6, equals 24 square centimeters. An equation appears, reading, one-half of 8, times 6, equals 24 square centimeters. The prism's base is marked, 24 square centimeters. Then, it rotates to a 3 dimensional view. TIM: Now, the height of our prism is 10 centimeters. The area of our base times the height is... 240 cubic centimeters. That's the volume! An equation appears, reading, 24 square centimeters, times 10 centimeters, equals 240 cubic centimeters. TIM: This formula works with prisms with bases of any shape. On-screen, several different prisms appear. TIM: You just have to use the proper formula to find the area of that base, and then multiply that by the prism's height. On-screen, the prisms rotate to show their bases. TIM: There we are; the volume of prisms. Moby juggles three glass prisms. TIM: Stop that! You're going to break them! Moby stops juggling and the prisms fall. 2 of them shatter. TIM: Well, at least one of them didn't break. On-screen, the last prism shatters. Category:BrainPOP Transcripts Category:BrainPOP Math Transcripts